TOLEDO, Ohio — A 4-year-old girl who went through two years of cancer treatments isn’t being allowed to go on a Make-A-Wish trip to Disney World because her father said she’s in remission and the trips should go to children who are sicker than his daughter.

The young girl, McKenna May of Haskins, had the trip postponed twice while was undergoing treatment for leukemia and finally was set to go in August when the father refused to sign off on the trip, the girl’s mother and grandmother said Thursday.

The family said Make-A-Wish requires signatures from both parents if either have visitation rights or is listed on the birth certificate. McKenna’s parents never married or lived together. Her grandmother said the father only recently received visitation privileges.

McKenna’s mother and grandmother are now collecting donations at local businesses to pay for the trip to Disney on their own. Money has poured in since their story spread beyond northwest Ohio. They haven’t told McKenna why the Make-A-Wish trip was canceled.

“We’ve told her we’re still going to Disney, just not when she thought it was happening,” said her grandmother, Lori Helppie. “We don’t want her judge her father.”

Her father, William May of Toledo, said donations made to the organization should help those who are terminally ill.

“Spend the money on a child who this might be their last memory,” May said Thursday. “Kids who are only going to live a year or six months.”

The girl’s grandmother said that McKenna has had a rough two years and won’t be judged to be free of cancer until five years after her last treatment, which was last month.

McKenna was diagnosed with leukemia in April 2010, just before she turned two. Chemotherapy treatments affected her speech and immune system, and she had three extended stays in the hospital. She also broke her leg in a fall. Doctors told the family that it would better to wait to go to Disney until McKenna was done with treatment, Helppie said.

“She’s been through quite a bit,” Helppie said. “We have had quite the journey getting her back to being like every other 4-year-old.”

McKenna’s mother, Whitney Hughes, said she’s overwhelmed that so many people have reached out to help. The family expects that they’ll soon have enough money to go to Disney. It’s something McKenna has talked about for months, her mom said.